Huge Decision of the Week: Broncos-Colts, Week 3

TJ JohnsonSep 29, 2010 1:00 PM

Note: Each Wednesday, we take a look at a critical coaching decision from the prior week’s game that had an impact on the final score—from a statistical point.

Most coaches play it safe. Too safe. They’d rather make a decision that likely won’t be criticized versus making a decision that has even the slightest potential for criticism from media, fans, and bloggers who still listen to Whitesnake and write from their parents’ basement.

Josh McDaniels does not—nor will he ever—play it safe. A graduate of the Belichick School of Take-This-And-Shove-It, he’s never met a 4th-and-short that he wouldn’t spit on.

I, for one, wouldn’t have it any other way.

Last week against the Colts, McDaniels once again provided us with ample opportunities to second guess his decisions. And once again he provided us with a textbook example of why going for it on 4th down, deep in your opponent’s territory, is usually the right move.

In order to analyze McDaniels’ decision, as always, we’ll split wide our two diva receivers, probability and Expected Points Value (EPV). So let’s get right to it.

By far, the most talked about decision last week came at the 8:46 mark of the 4th quarter. The Broncos were down 20-13 at the time, facing a 4th-and-3 at the Colts’ 12-yard line. As we know, Josh McDaniels faced two mutually-exclusive (it’s one or the other) decisions:

1) Go for the 1st down
2) Kick the field goal

Should McDaniels have just taken the points? The conservative coach (let’s call him Marty Schottenheimer since we all hate the Chiefs) would have surely gone with the field goal in the hopes that it would give his team a morale boost over the possibility of being mentally deflated if the team didn’t get a first down. After the game, a guy like Marty might say, “You never take points off the board.”

That sounds nice—even almost quaint. But for the love of Don Dokken, let’s at least bring some of this coach-speak into the 21st century after looking at some good old-fashioned math.

The Decision

For the decision McDaniels was facing, I’m using the following probability assumptions:

In 2009, teams were 44.57% on 4th downs in which they faced 3 to 5 yards

Teams were 83.62% when attempting field goals of 30-39 yards

As I mentioned last week, instead of using the average for all teams in 2009, one might want to consider the 4th-down percentage for an individual team. In this case, I could have chosen the Broncos’ 4th-down-and-short percentage from last year or this year. However, I chose not to because this year’s Broncos are not last year’s Broncos and I’m not totally comfortable with such a small sample size to draw from. So I’m sticking with the overall average.

And just like last week, let’s use Brian Burke’s EP values over at Advanced NFL Stats (A quick note: visit Burke’s site one time and you will already be several standard deviations smarter than the average Raiders fan).

Burke’s EP values tell us that we can expect the following values under these scenarios:

EPV of getting a 1st down and facing a 1st-and-goal at the Colts’ 9-yard line: 4.83

EPV of getting a FG: 2.3 (due to the Colts’ subsequent EP value after kickoff

EPV of turning the ball over and facing a Colts 1st-and-10 from their own 12-yard line: .11

EPV of missing the field goal and facing a Colts 1st-and-10 from the their own 20-yard line: -.34 (the Colts gets the ball where it’s placed, not snapped)

Now, let’s apply a probability equation (using our previous percentage assumptions and Burke’s EP values) to both going for the FG and the 1st down:

1. Going For the Field Goal:
(.8362 x 2.3)+((1-.8362) x (-.34) = 1.87 Expected Points
*Here we assume there’s an 83.62%% chance of making the field goal.

In both of these equations, we are simply applying the percentage chance of each event likely happening by the expected value of each event. We can see that the EPV of going for the 1st down is higher than going for the safer field goal.

After three weeks of this, you probably don’t even need to ask why going for the 1st down is a better call. But I know there are some Raiders fans who frequent this blog, so let’s review again. What is essentially happening with these equations is that the conversion rate on 4th-and-3 in the NFL is somewhat high. And the EP value of being that far into your opponents’ territory is worth more than a field goal in the long run. Thus, the value of a field goal, even a field goal with an 83.62% chance of success, just doesn’t yield enough expected points.

You Wanna Wear the Hoodie? Well, Do Ya, Punk?

Another way to think about this problem is from the perspective of McDaniels himself. So, put on your hoodie and baseball cap. Now ask yourself, “How sure would I need to be of getting the 1st down in order to justify going for it?”

Here what we do is simply take the same equation, but instead of plugging in our probabilities, we solve for it as a variable. Come on, Raiders fans, a little algebra never hurt anyone. We know that the percentage chance also has to yield a greater EP value than our alternative, which as we know is 1.87 EP. So here’s how we set up the equation:

(p*4.83)+((1-p)*(.11)) = 1.87

This equation can be further refined by stating 4.83p+1.11-.11p = 1.87

Now we simply solve for our probability. The answer, of course is 37.29%.

Yes, you read that correctly. If you are an NFL head coach, facing a 4-and-3 from your opponent’s 12-yard line, you would go for the 1st-down if you reasonably thought your team had a chance better than 37% of getting the 1st down.

Now how do you feel about McDaniels’ decision? Still think he made a bad call? I would hope not. If you don’t believe that Kyle Orton and Denver’s offense can get a 1st down in this situation at the approximate rate of once in three attempts, then you probably shouldn’t be a coach. Perhaps a blogger, but never ever should you think about buying a hooded sweatshirt, buddy.

Let’s not forget that the Broncos got the ball back on the very next drive and scored the field goal anyway. Why? The numbers were on their side. McDaniels made the correct call.

McDaniels wasn’t taking points off the board. He was trying to put the most points on the board when the odds were in his favor.
____________________________________________________________________________________If you like to see The Dude slack off 24/7, you can always follow him on Facebook and Twitter.

Chi, no worries. I was just messing with you. Your thoughts are great. And now I understand what you mean. You are very right. The big assumption behind EPV is that a team is trying to maximize its score. I see many instances, specifically under 2:00 when this is the case. Absolutely.

@DCJ: It&#8217s great to see you again. Sorry we didn&#8217t announce this with a big presser. I&#8217m glad you found us.

You know, since it&#8217s only three games, we could easily run those EPV values and remove the outliers, don&#8217t you think?

Posted by TJ Johnson on 2010-10-02 02:06:31

Chibronx,

Ha Ha, absolutely no offense taken. Regarding the duel, violence is not the answer. I suspect we&#8217re both used to being the smartest person in the room, so I have a nice collection of bruises on my shins from my wife&#8217s kicks under the table. I keep telling her violence is not the answer too. She says I need a healthy dose of humility. It&#8217s very hard to not correct fallacies isn&#8217t it?

Posted by Ponderosa on 2010-10-01 15:47:57

TJ, I&#8217ve been misunderestimated. Looking at EPV per player&#8212very interesting. But I was talking more about looking at the distribution of the EPV for everybody. In some game situations, the 50th percentile EPV might be 2, but you&#8217d find there&#8217s a much, much higher chance of it going to 6, and a low chance of it being anything below 1. Do you see what I&#8217m saying? The EPV could be distributed in a way that makes it a good decision to do something that DOES NOT maximize expected EPV, if the real point is to avoid a catastrophe, rather than maximize score over the longer-term.

Does this make sense? I could do something silly and model some scenarios. Using the knowledge I got at the academy of the streets, where I keep it real.

And Ponderosa&#8212did I really just lecture someone in the hard sciences about math? If we were at a party, you should have dumped a drink on my head. If we were in the 19th century, you would have been entitled to a duel.

Posted by Chibronx on 2010-10-01 14:14:11

I&#8217m a little late to the party (story of my life&#8212the cool kids never tell me where they&#8217ll be hanging) but glad I found you. I was thinking about the EPV the past couple days. As you sum up so nicely, the 4th quarter attempt was pretty much a no brainer, but I&#8217ve been pondering the run EPV for the 4th and goal from the one.

While I&#8217ve not done the numbers yet, my impression is that the abyssmal ypc average of the run game is actually inflated by one or two outlier runs. In fact, I wonder if the running game has a negative EPV for the Broncos. My suspicion is that removing the longest run will show the Broncos would have been better off taking the 3 points rather than making another attempt to run it in.

Posted by DCJ on 2010-10-01 06:35:03

Thanks for all your comments, everyone.

@ asisn, drew, ralph, sobchak: I love seeing your comments. They are just as entertaining as reading my own stuff. Keep it up.

@ Chibronx: Good points, all, although you know you academics always have to be the smartest guys in the room <img alt="wink" height="19" src="http://www.singernet.com/images/smileys/wink.gif" style="border:0;" width="19">!!!

Won&#8217t get much argument from me. Models are made to be broken, although I do like my model quite nicely. I like your point about Manning probably being in the highest quartile. Would be interesting to get the numbers on Manning for his career in these situations to better put a EPV on that. Still, I think it would show that going for it would still be a better move.

@Sadaraine: Good to have you back. I don&#8217t see your comments as detracting. Momentum is a big part of the game. If it weren&#8217t there would be no such things as an Elway comeback, would there? For those of us who have played sports at any level, we all know the sensation of momentum. Still, I think the best move was going for it. Both from a numbers and a momentum standpoint&#8212to recapture momentum. I like your point about the fade. Did not like the call at all.

Posted by TJ Johnson on 2010-10-01 03:40:47

I&#8217ll be the detractor here&#8230I said this on mhr too: Momentum is key to the game of football. All the stats in the world can&#8217t account for the emotional implications of momentum in a football game. I see it all the time and it is the one reason why I would have kicked the FG. The points help the defense&#8230the points help the offense, the points help the ST.

Now, if you take out emotions and play Madden, then I go for it on 4th and 3, but I sure as hell don&#8217t run a fade hot route on the weak side. You gotta throw the crossing patterns or a weak side out route all day long.

Posted by Sadaraine on 2010-09-30 20:01:50

Good stuff, good stuff. What do you know&#8212Josh McDaniels really IS smarter than I am!

Posted by broncosmontana on 2010-09-30 11:23:58

Great points Chibronx!

As a scientist I love the cool chill of numbers and equations since they have no bias or emotion. The application of equations and choice of what information to include however colors the conclusions significantly. You&#8217re quite right to observe that the Colts chances on first and 10 are demonstrably different than the Lions in the same situation. I think McD understands that too which also factored into his decision which I applaud and understand.

Medicine finally began to be a science when statistics and epidemiology were applied in the late 19th century. I love that football is being scrutinized from a wealth of statistical data because it helps me enjoy the game even more.

Posted by Ponderosa on 2010-09-29 21:21:28

Ponderosa,

I like TJ&#8217s work, too, and I think this analysis is pretty neat. It certainly confirms what I said at the time.

But math isn&#8217t inherently objective. Any charlatan can take the formulae, bend the assumptions to his will, then spit out a cherry-picked analysis and claim that science validates him.

My main curiousity in the EPV work is what it would look like if we started to look at the probability distribution behind each EPV in terms of game situations. The EPV numbers on advanced nfl stats are point estimates, the median from all of the possibilities. For examples, the Colts would have an EPV of .34 with a 1st and 10 on their own 20. The EPV is the 50th percentile projection. But what if the 40th percentile projection was .33, and the 60th percentile projection was 3.0? That makes kicking the field goal look lots worse.

Not to harsh on the dude, of course. He does a good job with this stuff. But there is always room for debate and questioning assumptions.

End of mini-rant.

Posted by Chibronx on 2010-09-29 20:45:20

TJ - as always thanks for the math behind the calls McDaniels&#8217 makes.

What we&#8217re seeing here from Bill Belichick, Sean Payton and McD is cultural and philosophical shift in offensive play-calling. You always see a Bell Curve in behavioural changes, and Belichick, Payton and McD are the early adoptors of going for it on fourth down, with the mainstream media and commenters at the DP yet to catch up on the new way of doing things.

Aside from the lack of execution, which is fixable, McD&#8217s fourth down calls have been more than justified by the numbers and our old friend, EPV, and I see no reason for him to change that.

Posted by orangecrushuk on 2010-09-29 20:37:06

Sweet

Posted by SobchakBronco on 2010-09-29 20:03:49

Sobchak, I realize we&#8217re only 3 weeks in here - so it&#8217s early, but that is definitely the leader in the clubhouse for Comment of the Year.

Posted by Douglas Lee on 2010-09-29 19:37:56

Thanks again TJ for the precision and objectivity of mathematical certainty. I believe McD just understands these probabilities due to his great football insight. I really believe his coaching decisions have been very astute. The criticisms he receives are born of prior prejudice towards him about personnel decisions and the situation he was thrust into from the start. Now admittedly, his first year as a head coach wasn&#8217t perfect, he made some mistakes, but I think this year will show many how perfectly fit he is for this job and this team. The transformation this team is undergoing is one where the immediate gains are less relevant than the long term changes.

I don&#8217t care how players no longer with the Broncos are doing with their current teams. There are sound decisions made by the head coach which factor in information not known to the common fan that determine relative value to this team. I wish them well, but they didn&#8217t belong here for where we&#8217re headed. Different teams have different priorities and needs. I&#8217m happy that McD is confident in what he wants for the vision he&#8217s decided upon for the Broncos.

Posted by Ponderosa on 2010-09-29 19:22:48

Math > mile high magic

Posted by SobchakBronco on 2010-09-29 19:04:51

TJ, great insight as usual. Thank you for your effort. In the moment, while watching the game, I thought that he really had no other choice. You are down 20-13 @ the 12. Make the field goal, and you&#8217re down by 4 and you still need to get into the endzone. You can&#8217t assume that you are going to get a better shot (from the 12)than that, or that you are going to get another shot at at all (fumble, int, 3/4 and out).

Drewthorn, totally agree. I think those that criticize his &#8220arrogance&#8221 may be enlightened by this. Is it arrogance, or an educated, calculated decision? I would think the latter.

Posted by RalphW on 2010-09-29 17:49:31

Thanks, TJ. I&#8217ve always enjoyed these.

Here&#8217s a probability to ponder: what&#8217s the likelihood that the same crew who are intensely criticizing McD for these decisions would also be intensely criticizing his arrogance for thinking red zone FG&#8217s would beat the great Peyton Manning? I&#8217m guessing near 100%. What&#8217s great about your work is that it makes objective sense out of a game that is almost entirely subjective (and its that subjective nature that allows people to draw what ever conclusion they are intent on drawing). If there was a way to assign actual value to the reality and brilliance of Peyton Manning, I&#8217m sure the math would emphatically show that McD would have been utterly foolish to not go for it in both situations. Peyton Manning doesn&#8217t give a rat&#8217s rear about the nature of his opponents psyche&#8212he&#8217s made a career of smirking at his opponents&#8217 &#8216momentum&#8217&#8212and that Austin Collie strike was virtually inevitable (and not at all unlike the strike to Clark that undid the Broncos late bid last year). A loss is a loss by any other name&#8230

Posted by Drewthorn on 2010-09-29 17:16:45

Nice stuff TJ and once again the numbers don&#8217t lie. Glad you&#8217re still finding time to put this drivel together instead of slacking off 24/7 <img alt="wink" height="19" src="http://www.singernet.com/images/smileys/wink.gif" style="border:0;" width="19">.